آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 126 |
| تعداد مقالات | 1,601 |
| تعداد مشاهده مقاله | 1,813,361 |
| تعداد دریافت فایل اصل مقاله | 1,684,555 |
On spectral properties of neighbourhood second Zagreb matrix of graph | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 10، شماره 2، شهریور 2025، صفحه 275-293 اصل مقاله (448.35 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28424.1546 | ||
| نویسندگان | ||
| Sasmita Barik* ؛ Piyush Verma | ||
| School of Basic Sciences, IIT Bhubaneswar, Bhubaneswar, 752050, India | ||
| چکیده | ||
| Let $G$ be a simple graph with vertex set $V(G)=\{1,2,\dots,n\}$ and $\delta(i)= \sum\limits_{\{i,j\} \in E(G)}d(j)$, where $d(j)$ is the degree of the vertex $j$ in $G$. Inspired by the second Zagreb matrix and neighborhood first Zagreb matrix of a graph, we introduce the neighborhood second Zagreb matrix of $G$, denoted by $N_F(G)$. It is the $n\times n$ matrix whose $ij$-th entry is equal to $\delta(i)\delta(j)$, if $i$ and $j$ are adjacent in $G$ and $0$, otherwise. The neighborhood second Zagreb spectral radius $\rho_{N_F}(G)$ is the largest eigenvalue of $N_F(G)$. The neighborhood second Zagreb energy $\mathcal{E}(N_F)$ of the graph $G$ is the sum of the absolute values of the eigenvalues of $N_F(G)$. In this paper, we obtain some spectral properties of $N_F(G)$. We provide sharp bounds for $\rho_{N_F}(G)$ and $\mathcal{E}(N_F)$, and obtain the corresponding extremal graphs. | ||
| کلیدواژهها | ||
| 05C50؛ 05C09؛ 05C92 | ||
| مراجع | ||
|
[1] R.B. Bapat, Graphs and Matrices, Second Edition, Hindustan Book Agency, New Delhi, 2018.
[2] A.E. Brouwer and W.H. Haemers, Spectra of Graphs, Springer, New York, 2011. https://doi.org/10.1007/978-1-4614-1939-6
[3] L.V. Collatz and U. Sinogowitz, Spektren endlicher grafen, Abh. Math. Semin. Univ. Hambg. 21 (1957), 63–77. https://doi.org/10.1007/BF02941924
[4] J. Day and W. So, Singular value inequality and graph energy change, The Electron. J. Linear Algebra 16 (2007), 291–299.
[5] T. Došlić, B. Furtula, A. Graovac, I. Gutman, S. Moradi, and Z. Yarahmadi, On vertex-degree-based molecular structure descriptors, MATCH Commun. Math. Comput. Chem. 66 (2011), no. 2, 613–626.
[6] H.A. Ganie, U. Samee, S. Pirzada, and A.M. Alghamadi, Bounds for graph energy in terms of vertex covering and clique numbers., Electron. J. Graph Theory Appl. 7 (2019), no. 2, 315–328. https://dx.doi.org/10.5614/ejgta.2019.7.2.9
[7] M. Ghorbani and M.A. Hosseinzadeh, A note of Zagreb indices of nanostar dendrimers, Optoelectron. Adv. Mat. 4 (2010), no. 11, 1877–1880.
[8] I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forsch. Graz. 103 (1978), 1–22.
[9] I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86 (2013), no. 4, 351–361. https://doi.org/10.5562/cca2294
[10] I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83–92.
[11] I. Gutman, E.A. Martins, M. Robbiano, and B. San Martin, Ky fan theorem applied to Randi´c energy, Linear Algebra Appl. 459 (2014), 23–42. https://doi.org/10.1016/j.laa.2014.06.051
[12] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total ϕ-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538. https://doi.org/10.1016/0009-2614(72)85099-1
[13] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, United Kingdom, 2012.
[14] A. Ilic, M. Ilic, and B. Liu, On the upper bounds for the first Zagreb index, Kragujevac J. Math. 35 (2011), no. 1, 173–182.
[15] N. Jafari Rad, A. Jahanbani, and I. Gutman, Zagreb energy and Zagreb Estrada index of graphs, MATCH Commun. Math. Comput. Chem. 79 (2018), no. 2, 371–386.
[16] X. Li, Y. Shi, and I. Gutman, Graph Energy, Springer, New York, 2012.
[17] M. Liu and B. Liu, The second Zagreb indices of unicyclic graphs with given degree sequences, Discrete Appl. Math. 167 (2014), 217–221. https://doi.org/10.1016/j.dam.2013.10.033
[18] R. Liu and W.C. Shiu, General Randić matrix and general Randi´c incidence matrix, Discrete Appl. Math. 186 (2015), 168–175. https://doi.org/10.1016/j.dam.2015.01.029
[19] S. Mondal, S. Barik, N. De, and A. Pal, A note on neighborhood first Zagreb energy and its significance as a molecular descriptor, Chemom. Intell. Lab. Syst. 222 (2022), Article ID: 104494. https://doi.org/10.1016/j.chemolab.2022.104494
[20] S. Mondal, N. De, and A. Pal, On some new neighbourhood degree based indices, ACTA Chemica IASI 27 (2019), no. 1, 31–46.
[21] V. Nikiforov, The energy of graphs and matrices, J. Math. Anal. Appl. 326 (2007), no. 2, 1472–1475. https://doi.org/10.1016/j.jmaa.2006.03.072
[22] S. Nikolić, G. Kovačević, A. Miličević, and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), no. 2, 113–124.
[23] S. Pirzada, H.A. Ganie, and U.T. Samee, On graph energy, maximum degree and vertex cover number, Le Matematiche 74 (2019), no. 1, 163–172.
[24] S. Pirzada and S. Khan, On Zagreb index, signless Laplacian eigenvalues and signless Laplacian energy of a graph, Comp. Appl. Math. 42 (2023), no. 4, Article number: 152. https://doi.org/10.1007/s40314-023-02290-1
[25] B.R. Rakshith, On Zagreb energy and edge-Zagreb energy, Commun. Comb. Optim. 6 (2021), no. 1, 155–169. https://doi.org/10.22049/cco.2020.26901.1160
[26] H. Shooshtary and J. Rodriguez, New bounds on the energy of a graph, Commun. Comb. Optim. 7 (2022), no. 1, 81–90. https://doi.org/10.22049/cco.2021.26999.1179
[27] R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, John Wiley & Sons, United States, 2008.
[28] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947), no. 1, 17–20. https://doi.org/10.1021/ja01193a005
[29] H. Yuan, A bound on the spectral radius of graphs, Linear Algebra Appl. 108 (1988), 135–139. https://doi.org/10.1016/0024-3795(88)90183-8
[30] F. Zhan, Y. Qiao, and J. Cai, On edge-Zagreb spectral radius and edge-Zagreb energy of graphs, Linear Multilinear Algebra 66 (2018), no. 12, 2512–2523. https://doi.org/10.1080/03081087.2017.1404960
[31] B. Zhou, On the spectral radius of nonnegative matrices, Australas. J. Combin. 22 (2000), 301–306.
[32] B. Zhou, I. Gutman, and T. Aleksic, A note on Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 60 (2008), no. 2, 441–446. | ||
|
آمار تعداد مشاهده مقاله: 778 تعداد دریافت فایل اصل مقاله: 2,387 |
||